Filters, such as bandpass filters, have numerous applications in communications and electronics. For example, in wireless communications a given frequency band must accommodate many wireless users. To accommodate so many users, stringent bandpass filtering requirements must be achieved because of the crowded frequency allocations provided.
At present, wireless handsets use fixed-tuned bandpass filters (BPFs) to meet their filtering specifications. The design of such filters is complicated because they must achieve the lowest possible passband insertion loss (I.L.) while simultaneously achieving a specified large out-of-band rejection. As a specific example, consider full band PCS CDMA handsets using fixed bandwidth filters. The PCS transmit (TX) band should have no more than −3.5 dB I.L. in-band (1850 to 1910 MHz in the U.S.) while having at least a 38.0 dB out-of-band rejection in the receive (RX) band (1930 to 1990 MHz range).
Further, this BPF must meet these specifications with a maximum constraint on height. A typical height constraint in present day handsets, for example, is 4.0 mm or less. To meet these demanding electrical requirements yet possess the smallest possible size and height, high order (>2nd order) fixed-tuned filters constructed from either individual coaxial resonator elements or monoblock structures are usually necessary. In addition, to satisfy out-of-band rejection specifications, a transmission zero is usually required, increasing I.L. at the band edge. Because of variations in ceramics and fabrication tolerances, vendors must individually adjust the characteristics of fixed-tuned filters during their manufacture, driving costs higher.
Moreover, if more than one frequency band were to be supported (e.g., supporting the PCS bands in the U.S., Korea, and India) multiple fixed-tuned BPFs would be necessary, requiring extra switches which introduces additional loss. This is true, even if the power amplifier and low noise amplifier used have sufficient bandwidth to operate over these multiple bands.
A tunable BPF would allow the use of one BPF over several bands, or of a lower order filter to cover a bandwidth wider than a required passband at any particular time. To provide the tunability in a tunable BPF, a component capable of providing a variable capacitance is typically used.
Several structures are presently used to implement a variable capacitor. For example, movable parallel plates have been used for many years as the tuner in home radios. However, such plates are far too bulky, noisy, and impractical for use in most modern applications.
Another alternative, the electronic varactor, is a semiconductor device that adjusts capacitance responsive to an applied voltage. Because the varactor is typically noisy and lossy, particularly in applications above 500 MHz, it is ineffective for high-frequency, low-loss applications where high performance is required.
Another alternative, a micro-electro-mechanical-system (MEMS) is a miniature switching device that may switch between capacitors responsive to an applied control signal. It, however, is costly, difficult to manufacture and of unproven reliability. In most cases, it provides discrete tuning, in that a system must select between a finite (and small) number of fixed capacitors.
Ferroelectric tunable capacitors are another alternative that has been attempted. Ferroelectric (F-E) materials are a class of materials, typically ceramic rare-earth oxides, whose prominent feature is that their dielectric constant (κ), and as a consequence, the electric permittivity (κ) changes in response to an applied slowly varying (DC or low frequency) electric field. The relationship of the dielectric constant (κ) and the electric permittivity (ε) of a material is given as follows:ε=κε0                 where ε0 is the electric permittivity of a vacuum. At present, there are several hundred known materials that possess F-E properties. In a typical F-E material, one can obtain a range in κ by a factor of as much as approximately 3:1. The required DC voltage to generate such a change in κ depends on the dimensions of the F-E material over which a DC control voltage is applied. As a result of their variable dielectric constant, one can make tunable capacitors using F-E materials, because the capacitance of a capacitor depends on the dielectric constant of the dielectric proximate the capacitor conductors. Typically, a tunable F-E capacitor is realized as a parallel plate (overlay), interdigital (IDC), or a gap capacitor.        
In known F-E variable capacitors, a layer of an appropriate F-E material, such as barium strontium titanate, BaxSr1-xTiO3 (BSTO) is disposed adjacent to one or both conductors of a capacitor. Depending upon the strength of the electric field applied to the F-E material and the intrinsic properties of the F-E material selected, the capacitance changes. Typically, below the Curie temperature, Tc, of the F-E film, the F-E material is in the ferroelectric state and will exhibit hysteresis in its response to a changing electric field. Above Tc, F-E material is in the paraelectric state and will not exhibit hysteresis. Thus, one generally picks an F-E material whose Tc is lower than the expected operating temperature so as to operate in the paraelectric state, avoiding the hysteresis effects of the ferroelectric state.
However, conventional F-E variable capacitors have proven to be too lossy for use in insertion-loss-sensitive applications such as handsets. Moreover, these devices often perform unpredictably, preventing optimal design, construction, and use of F-E tunable filters.
Duplexers are used in CDMA technology to separate the Tx and the Rx frequencies into their respective signal paths. Duplexers typically comprise two bandpass filters. Each filter selects either the Tx or the Rx frequency signal to be passed. The filters are coupled at one end, forming a common port. This common port is typically coupled to an antenna or a diplexer for sending transmit signals and receiving receive signals.
Strict insertion loss and out-of-band rejection requirements are the primary requirements that influence the design of duplexers for use in loss sensitive applications, for example, in wireless handsets. Other electrical and mechanical specifications must also be satisfied, such as, for example, size and height requirements.
Accordingly, there is a need in the art for improved tunable F-E filters capable of providing a tuning range over a desired frequency range with low I.L. and high out-of-band rejections and methods for designing the same. These filters could then be used to make tunable duplexers.